Get the element field from a type-sequence.
This is an ordinary field accessor created by fty::defprod.
Function:
(defun type-sequence->element$inline (x) (declare (xargs :guard (typep x))) (declare (xargs :guard (equal (type-kind x) :sequence))) (let ((__function__ 'type-sequence->element)) (declare (ignorable __function__)) (mbe :logic (b* ((x (and (equal (type-kind x) :sequence) x))) (type-fix (std::da-nth 0 (cdr x)))) :exec (std::da-nth 0 (cdr x)))))
Theorem:
(defthm typep-of-type-sequence->element (b* ((element (type-sequence->element$inline x))) (typep element)) :rule-classes :rewrite)
Theorem:
(defthm type-sequence->element$inline-of-type-fix-x (equal (type-sequence->element$inline (type-fix x)) (type-sequence->element$inline x)))
Theorem:
(defthm type-sequence->element$inline-type-equiv-congruence-on-x (implies (type-equiv x x-equiv) (equal (type-sequence->element$inline x) (type-sequence->element$inline x-equiv))) :rule-classes :congruence)
Theorem:
(defthm type-sequence->element-when-wrong-kind (implies (not (equal (type-kind x) :sequence)) (equal (type-sequence->element x) (type-fix nil))))